Better Two-Round Adaptive Multiparty Computation.

The only known two-round multi-party computation protocol that withstands adaptive corruption of all parties is the ingenious protocol of Garg and Polychroniadou [TCC 15]. We present protocols that improve on the GP protocol in a number of ways. First, concentrating on the semi-honest case and taking a different approach than GP, we show a two-round, adaptively secure protocol where:Only a global i.e., non-programmable reference string is needed. In contrast, in GP the reference string is programmable, even in the semi-honest case.Only polynomially-secure indistinguishability obfuscation for circuits and injective one way functions are assumed. In GP, sub-exponentially secure IO is assumed. Second, we show how to make the GP protocol have only RAM complexity, even for Byzantine corruptions. For this we construct the first statistically-sound non-interactive Zero-Knowledge scheme with RAM complexity.